Physics · Science General

Collisions, Momentum and Kinetic Energy

385 Questions

Collisions, momentum, and kinetic energy questions analyze the principles of elastic and inelastic impacts. They require calculating mass, velocity, and conserved energy during physical interactions. These foundational physics topics are essential for most government engineering and general science examinations.

Elastic collisionsInelastic collisionsMomentum calculationKinetic energy principlesVelocity after impact

Collisions, Momentum and Kinetic Energy Questions

Multiple choice modelling collisions collisions momentum work, energy and power physics

A mass $m _1$ moves with a great velocity. It strikes another mass $m _2$ at rest in a head on collision and comes back along its path with a low speed after collision. Then :

  1. $m _1 > m _2$
  2. $m _1 = m _2$
  3. $m _1 < m _2$
  4. there is relation between $m _1$ and $m _2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a head-on elastic collision between a small projectile and a more massive target, the projectile will bounce back with low speed and the massive target will be given a very small velocity. Hence, $m _1 < m _2$

Multiple choice modelling collisions collisions momentum work, energy and power physics

A body moving towards a body of finite mass at rest collides with it. It is possible that :

  1. both bodies come to rest

  2. the stationary body remains stationary and the moving body rebounds.

  3. the moving body stop and the body at rest start moving.

  4. all of the above are correct.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From the very fundamental law of collision we know that in a collision momentum of the system is conserved .
Therefore the only possible option is C.

Multiple choice modelling collisions collisions momentum work, energy and power physics
Collision is a physical process in which two or more objects, either particle masses or rigid bodies, experience very high force of interaction for a very small duration. It is not essential for the objects to physically touch each other for collision to occur. Irrespective of the nature of interactive force and the nature of colliding bodies, Newton's second law holds good on the system. Hence, momentum of the system before and after the collision remains conserved if no appreciable external force acts on the system during collision.
The amount of energy loss during collision, if at all, is indeed dependent on the nature of colliding objects. The energy loss is observed to be maximum when objects stick together after collision. The terminology is to define collision as 'elastic' if no energy loss takes place and to define collision as 'plastic' for maximum energy loss. The behaviour of system after collision depends on the position of colliding objects as well. A unidirectional motion of colliding objects before collision can turn into two dimensional after collision if the line joining the centre of mass of the two colliding objects is not parallel to the direction of velocity of each particle before collision. Such type of collision is referred to as oblique collision which may be either two or three dimensional.

Which of the following collision is one-dimensional?

  1. Head on collision

  2. Perfectly elastic collisions

  3. Perfectly inelastic collisions

  4. Oblique collisions
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Head-on collision is always one dimensional the centre of mass of each body move in the same direction after collision as they were moving before collision. 

Multiple choice modelling collisions collisions momentum work, energy and power physics

Two bodies of identical mass $m$ are moving with constant velocity $v$ but in the opposite direction with velocity of $A$ which is equal to $0.3\ m/s$. After collision the two balls come to rest when the velocity of $B$ is:

  1. $0.15\ m/s$
  2. $1.5\ m/s$
  3. $-0.15\ m/s$
  4. $none\ of\ these$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice modelling collisions collisions momentum work, energy and power physics

Which one of the following statements is true?

  1. Momentum is conserved in elastic collision but not in inelastic collisions

  2. Total kinetic energy is conserved in elastic collisions but momentum is not conserved in elastic collision

  3. Total kinetic energy is not conserved but momentum is conserved in inelastic collisions

  4. Kinetic energy and momentum both are conserved in all types of collisions
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The law of conservation of momentum is true in all type of collisions, but kinetic energy is conserved only in elastic collision. The kinetic energy is not conserved in inelastic collision but the total energy is conserved in all type of collisions.

Multiple choice modelling collisions collisions momentum work, energy and power physics

If one body collides with another body of same mass at rest inelastically, the ratio of their speeds after collision shall be-

  1. e
  2. $\displaystyle \frac{1-e}{1+e}$
  3. $\displaystyle \frac{1+e}{1-e}$
  4. $\displaystyle \frac{1}{e}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let ${u} _{1}$ be the speed of body initially before collision.
${u} _{2}=0$
Let ${v} _{1}$ be speed of particle 1 after collision and ${v} _{2}$ be speed of particle 2 after collision.
Using law of conservation of momentum
$m{u} _{1}=m{v} _{1}+m{v} _{2}$
${u} _{1}={v} _{1}+{v} _{2}$
Coefficient of restitution will be given by
$e=\dfrac{{v} _{2}-{v} _{1}}{{u} _{1}}=\dfrac{{v} _{2}-{v} _{1}}{{v} _{1}+{v} _{2}}$
$e{v} _{1}+e{v} _{2}={v} _{2}-{v} _{1}$
Dividing throughout by ${v} _{2}$ and rearranging leads to
$\dfrac{{v} _{1}}{{v} _{2}}=\dfrac{1-e}{1+e}$

Multiple choice modelling collisions collisions momentum work, energy and power physics

Which of the following statement is true?

  1. Kinetic energy and momentum both are conserved in all types of motion.

  2. Momentum is conserved in elastic collision but not in inelastic collision.

  3. Total kinetic energy is not conserved but momentum is conserved in inelastic collision.

  4. Kinetic energy is conserved in elastic collision but not in inelastic collision.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Linear momentum is conserved in elastic as well as inelastic collision but kinetic energy is conserved only in case of elastic collision but some kinetic energy is lost in inelastic collision.

Multiple choice modelling collisions collisions momentum work, energy and power physics

During collision
a) There is a change in momenta of individual bodies
b) The change in total momentum of the system of colliding particle is zero
c) The change in total energy is zero
d) The law of conservation of momentum is not valid

  1. only a & b are true

  2. only b & c are true

  3. a, b & c are true

  4. b, c & d are true
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Energy conservation is valid everywhere i.e. total energy is conserved everytime. In collision, the kinetic energy of the system may get lost. However, the momentum of the system is always conserved and so the change in the momentum of the system is zero.

Multiple choice modelling collisions collisions momentum work, energy and power physics

During "inelastic collision "

a) There is a loss of kinetic energy.
b) Some of the kinetic energy is used to deform the body.
c) Some of the kinetic energy is liberated as heat.
d) There is a loss of mass energy.

  1. Only a is true

  2. Only b and c are true

  3. a,b & c are true

  4. b, c & d are true
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We know that during an inelastic collision, there is a loss of kinetic energy, some of the kinetic energy is used to deform the body and some of the kinetic energy is liberated as heat. But their is no loss of mass-energy.

Multiple choice modelling collisions collisions momentum work, energy and power physics

During elastic collision which of the following things happens ?
a) The colliding bodies experience large force during small interval of time
b) The colliding bodies need not touch each other
c) The kinetic energy remain conserved 
d) The linear momentum remain conserved

  1. Only $a$ and $b$ happen
  2. Only $b$ and $c$ happen
  3. $a , b$ and $c$ happen

  4. All are true
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Kinetic energy is lost from a system of colliding objects because the collision transforms kinetic energy into other forms of energy - sound, heat and light energy. When the colliding objects don't really collide in the usual sense (that is when the collision force is a non-contact force), the system of colliding objects does not lose its kinetic energy and thus kinetic energy is conserved.
Since there is no external force , linear momentum of system will be conserved.
Also, the time of impact in elastic collision is very small and so the colliding bodies experience large force during small interval of time.
Hence all the statements are true.
Multiple choice modelling collisions collisions momentum work, energy and power physics

During an "elastic collision " , 
a) there is no loss of kinetic energy
b) the bodies are perfectly elastic
c) temporarily some of the kinetic energy is used to deform the bodies
d) after collision the bodies regain the original shape keeping the total energy constant

  1. only "a" is true

  2. a, c, d are true

  3. b, c, d are true

  4. a, b, c ,d are true
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In an elastic collision, e is equal to 1. Therefore, the kinetic energy used in causing deformation of the bodies is recovered completely in the reformation since the reformation is complete. So no energy is lost. 

Multiple choice modelling collisions collisions momentum work, energy and power physics

Identify the correct statements from the following :

a) The collisions between the nuclei and fundamental particles are considered as elastic collisions.
b) Emission of an alpha particle by $U^{235}$ is an "elastic collision".
c) The collision between two ivory balls is considered as " elastic collision".
d) A running man jumps into a train. It is an "elastic collision".

  1. Only a & b are true

  2. Only b & c are true

  3. a, b & c are true

  4. b, c & d are true
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A collision is considered elastic collision if the kinetic energy before collision is equal to the kinetic energy after collision.

In collision of nuclei and fundamental particles, unless there is emission of gamma rays, kinetic energy of the system remains constant.

In Alpha particle emission, energy is not being released in any other form. Hence kinetic energy of the system will remain same before and after the emission.

In collision of two ivory balls, the balls being extremely hard, no deformation happens and for most practical purposes energy is assumed to not being converted into any other form such as heat(which happens when there is friction or deformation).

In the case of a running man jumping on to the train, friction and deformation happens in order for the man to continue moving along with the train. Thus energy was converted into other forms. Hence, it is an example of inelastic.

Multiple choice modelling collisions collisions momentum work, energy and power physics

The co-efficient of restitution e for a perfectly elastic collision is

  1. $1$
  2. $0$
  3. $-1$

  4. infinity
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The co-efficient of restitution for a perfectly elastic collision is $e = 1$

The co-efficient of restitution for a perfectly inelastic collision is $e = 0$
The co-efficient of restitution for rest of the collisions is $0<e < 1$

Multiple choice modelling collisions collisions momentum work, energy and power physics

Two spheres of different masses moving in the same direction undergo perfect head on elastic collision.
Then,
a) Their velocities are interchanged if they are of same mass

b) If the heavier sphere were at rest before collision. it continues to be at rest after collision and the lighter sphere retraces its path with the same velocity

c) If the lighter sphere were at rest before collision, it moves with the velocity of the heavier sphere and the heavier sphere continues to move with its original velocity after collision.

d) If the lighter sphere were at rest before collision, it moves with double the velocity of the heavier sphere and the heavier sphere continues to move with its original velocity, after collision.

  1. a,b,c are correct

  2. a,b are correct

  3. b,c are correct

  4. a,b,d are correct
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A) Common result.
B) e.g Ball hitting a wall
C) $e= \dfrac{O-V}{V-V^{1}} = 1$
$V^{1} = 2V$
D) As in C